2011 | OriginalPaper | Buchkapitel
Laws of Large Numbers and Nearest Neighbor Distances
verfasst von : Mathew D. Penrose, J. E. Yukich
Erschienen in: Advances in Directional and Linear Statistics
Verlag: Physica-Verlag HD
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We consider the sum of power weighted nearest neighbor distances in a sample of size
n
from a multivariate density
f
of possibly unbounded support. We give various criteria guaranteeing that this sum satisfies a law of large numbers for large
n
, correcting some inaccuracies in the literature on the way. Motivation comes partly from the problem of consistent estimation of certain entropies of
f
.